Tag: fractal

If you’ve ever had the feeling “same shit, higher dimension”, I’m sure you’d fit right in on Fifth World Problems, a subreddit in the key of First World Problems, and a place for extradimensional beings to air their cosmic gripes.

I got 99 problems but a 4D hypercube ain't one

Most of the submissions and their respective commentary are childish lunacy, but among the smarter entries lie some fascinating thought experiments. I find myself stretching for a scientifically reasoned solution, if only I weren’t so limited by my inferior human mind!

Equally silly and clever, here are some of my favourites for your delectation and amusement:

My membrane girlfriend and I didn’t use protection when we collided and now we’re going to have a universe. I’m not ready to be a deity but my family is pro-existence. What do I do?

Minutes have stopped accumulating as hours. It’s now 4:237 PM and my boss still won’t let me punch out 🙁

I forgot my admin password and now my memories are read-only.

I hired a möbius stripper for a party but she finished her act with her clothes still on and I can’t get a refund.

My neutrinos were caught speeding, now my insurance is going up √-17 %

I am the very thing I am typing and am terrified that submitting myself will result in a collapse of my consciousness.

I was unwittingly assigned to be controlled by a modulation wheel. Now I sound like dubstep.

I forced the alive and dead versions of Schrödinger’s cat to mate. The resultant offspring has enslaved my family.

I accidntally dstroyd a prtty important lttr.

I commissioned an artist to paint me a fractal and I think he is just trying to milk this project out for more payment. Will he ever be done?

Any favourites of your own? Or any solutions, even? Post them over at Fifth World Problems or let’s talk them out in the comments.

This post is about one of the really cool things that happens when maths I don’t understand and technologies I don’t understand get together to make something awesome. Let us begin:

A typical fractal, made using the Mandelbrot set.

A fractal is a conceptual object that reveals further details about its shape ad infinitum, upon ever-closer inspection of it’s fabric. Think of the trunk of a tree sprouting branches, which in turn split off into smaller branches, which themselves yield twigs etc and you won’t go far wrong. In fact, fractals typically look like this thing to the right.

These infinitely complex shapes are ‘created’ by instructing graphics software to render the result of a simple mathematics formula. Until now, the result has been a 2D image – there’s no depth, shadow, perspective, or light sourcing. It is a truly abstract mathematical shape.

But since your home computer became powerful enough to do proper image rendering stuff, home hobbyists have begun to innovate on these formulae. For the first time, three dimensional fractals are able to be created with relative ease.

I can’t go into the maths, because you know, I’m not a total geek, but I do want to show you how beautiful some of these shapes are. Let’s run through some examples:

This is what you get by multiplying phi and theta by two.

More like a classic fractal with 0.5*pi to theta and 1*pi to phi.

This time multiplying angle phi by two, but not theta.

But we’re still looking at these things from outside. The really cool bit is when you start to zoom in. So let’s look at some of the high quality renders from the archives of Daniel White at his highly eclectic Skytopia, where I first learned of this phenomenon.

Make sure you click around on some of these thumbnails, yeah?!

If you’re anything like me, you’d be pretty excited at the idea of being able to create both beauty and complexity from something as simple as a few lines of code, and to then be able to explore your creation from every angle.

Then again, if you’re anything like me, you’d feel a bit frustrated that you’ll probably never be able to make something that awesome yourself. So let’s marvel at the wonder of Daniel’s creation as he takes us deep ‘Into the Heart of the Mandelbulb’.